Space of modular forms of level 2880, weight 1, and Character 2880.r

• Label: 2880.1.r
• Level: $2880$
• Weight: $1$
• Character orbit: 2880.r
• Rep. character: $\chi_{2880}(559,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $576$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2880.r (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 80 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(576\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2880, [\chi])\).

	Total	New	Old
Modular forms	80	8	72
Cusp forms	16	4	12
Eisenstein series	64	4	60

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	4	0	0	0

Trace form

\( 4 q - 4 q^{19} + 4 q^{49} - 4 q^{61} - 4 q^{85}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2880, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2880.1.r.a	$2880$	$1$	2880.r	80.k	$4$	$4$	$2$	$1.437$	\(\Q(\zeta_{8})\)	$D_{4}$	\(\Q(\sqrt{-15}) \)	None			✓	✓	720.1.r.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{8}^{3}q^{5}+(-\zeta_{8}-\zeta_{8}^{3})q^{17}+(-1+\cdots)q^{19}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2880, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2880, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 3}\)